Chapter 1

Introduction to Analytical Chemistry

Chemistry: Chemistry is that branch of science which deals with the study of matter. Anything

that having mass and occupy space is called matter. There are four different types of matter i.e.

Gas, liquid, solid and plasma. Gas is that type of matter having no proper shape and no proper

volume i.e. air, nitrogen gas etc. Liquid is that type of matter having proper volume but no

proper shape adopt the shape of the pot in that it is putted like water, milk etc. Solid is that type

of matter having proper shape and proper volume i.e. stone, book, wood etc.

Plasma is that type of matter which is in between solid and liquid. It is found on sun.

ANALYTICAL CHEMISTRY : The Science of Chemical Measurements.OrAnalytical chemistry is that branch of chemistry which deals with the analysis or characterization

of analyte species. Analyte is that species which is under consideration or observation or about

that we don’t know. Its chemical composition is unknown to us.

The process that we are using to get know about the chemical composition of analyte species is

called analysis. In analytical chemistry there are two types of analysis, one is known is

qualitative analysis and the other type is called quantitative analysis .

Qualitative analysis is used for identification or knowing the chemical nature of the analyte

species from which the analyte is made up, while the quantitative analysis is used to know about

the unknown amount of analyte species.

2.) Types of Questions asked in Analytical Chemistry

a.) What is in the sample? (Qualitative analysis)

b.) How much is in the sample? (Quantitative analysis)

c.) How pure is it? (Separation analysis)

Analysis can be done with the help of using analytical techniques. Analytical techniques are

valid procedures that are used for analysis. There are two groups of analytical techniques. One

group is called as Qualitative analytical techniques used for identification of chemical nature

of analyte species i.e. salt analysis, FTIR analysis, NMR analysis. While the other group of

analytical techniques called Quantitative analytical techniques used to know about the

unknown amount of analyte. Quantitative analytical techniques are further sub classified into

classical techniques, while the other group of Quantitative analytical techniques is called

Instrumental techniques. In case of classical techniques simple equipments like burette, pipette,

flasks, cylinder, balance etc are used, while in case of Instrumental techniques the modern

instruments are used to do analysis.

Classical techniques are further sub classified as volumetric techniques, gravimetric

techniques and separative techniques, while the instrumental techniques are sub classified as

spectroscopic techniques, electroanalytical techniques and separative techniques.

Volumetric techniques consist of a group of classical techniques based on volume measurement

therefore are called as volumetric techniques, it include acid base titration (neutralization

titration), redox titration, precipitation titration and complexomtric titration.

Gravimetric techniques is another class of classical techniques based on mass measurement like

precipitation, volatilization etc.

While the 3rd group of classical techniques is based on separation for purification purposes

include distillation, filtration, crystallization, sublimation, solvent extraction,

chromatography, electrophoresis etc.

Instrumental Techniques: It is a group of Quantitative analytical techniques used for analysis

of analyte species and can be practiced by using some instruments. Instrumental techniques are

further sub classified as spectroscopic techniques, electroanalytical techniques and

separative techniques.

Spectroscopic techniques are that kind of instrumental analytical technique in which

spectrophotometer is used as an instrument and it is used both for identification as well

quantification (determination the unknown amount) of analyte. It is based on interaction

of electromagnetic radiations with matter. Some time the matter absorbs or sometimes

emits radiations. So in spectroscopy we measure the magnitude of absorbed or emitted

radiations and then relate that magnitude of radiations with the concentration of analyte

species.

Electroanalytical techniques are that group of instrumental technique in that the

magnitude of electricity interacted with the analyte specie is measured with the help of

electrochemical cell. I.e. potentiometry, conductometry, voltammetry etc

Separative techniques are that group of instrumental technique in that the instruments like

HPLC, GC, Ion chromatograph etc are used for separation, purification identification as

well as quantification of analyte specie.

Units of Amount

Amount is that mass of solute which containing know number of particles i.e. atoms, ions or

molecule. In analytical chemistry different units of amount like mole, equivalent and formals are

used.

Mole:

Mole is a unit of amount and can be defined as, one mole is that amount which containing

Avogadro number (6.0221415 × 1023) of particles. It can be also defined as when the atomic

mass of an atom or ion or molecular mass of a molecule is expressed in grams, then that gram

atomic or molecular mass is called one mole amount and it will be containing Avogadro number

of particle.

Examples:

Carbon = 12amu = 12g = 1mole = 6.0221415 × 1023 carbon atoms

Sodium ion = 23amu = 23g = 1mole = 6.0221415 × 1023 Na+

Water = 18amu = 18g = 1mole = 6.0221415 × 1023 H2O molecules

In analytical Chemistry number of moles is calculated as below

Examples: Calculate the number of moles for 4g mass of NaOH.

Solution:

Using the above expression as we know

As we know Molecular mass of NaOH = 23+16+1 = 40amu

Put the values in the above expression

Number of moles of NaOH = 0.1 moles

It will be containing (0.1 x 6.0221415 × 1023) = 6.0221415 × 1022 molecules of NaOH

In case of solutions number of moles is calculated as

Example: Calculate the number of moles for a solution having concentration 0.1M and its total

volume is 250mL.

Solution: As we know

So putting the values in this expression as

Equivalent:

Equivalent is also a unit of amount and it can be defined as, one equivalent is that amount which

containing Avogadro number (6.0221415 × 1023) of reactive specie. In case of acid base reaction

reactive specie is hydrogen ion (H+) for acid and hydroxyl ion (OH-) for base, while in case of

redox reaction the reactive specie is the number of electron lost or gained. In analytical chemistry

number of equivalent can be calculated as below

Equivalent mass can be defined as molecular mass of the analyte divided by number of reacting

units as

Number of reacting units in case of acid base reaction is the number of hydrogen or hydroxyl

ions per molecule, while in case of oxidation reduction is the number of electron lost or gained

by an atom or molecule.

Examples: Calculate the number of moles for 8g mass of Na2CO3.

Solution:

Using the above expression as we know

As we know Na2CO3 on hydrolysis produce two hydroxyl ions so it

It means 53g of Na2CO3 containing Avogadro number (6.0221415 × 1023) of hydroxyl ion (OH-)

Now

In case of solutions number of equivalent is calculated as

Example: Calculate the number of equivalents for a solution having concentration 0.1N and its

total volume is 250mL.

Solution: As we know

So putting the values in this expression as

Formals

Formal is also a unit of amount similar to mole but in case of crystalline ionic compounds like

NaCl we are writing formula unit mass instead of molecular mass i.e.

Formula mass of NaCl = 23 + 35.5 = 58.5amu

Units of Concentration

Concentration is the ratio between the amount of solute and solvent. Solution is a mixture of

solute and solvent. In analytical chemistry for analysis solutions of different concentrations are

used. To prepare solutions of different concentrations there are different types of concentration

units like molarity, normality, formality, molality, %age solutions, ppm (parts per million), ppb

(parts per billion) etc are used in analytical chemistry.

Molarity

It is a unit of concentration and is denoted by “M”. It can be defined as the number of moles of solute dissolved per unit volume of solution

Mole is unit of amount and can be defined as

Substituting the values of no of moles of solute in above equation so

Rearranging the above expression as

As we know

1L = 1000ml, so replace volume in letter by volume in mL in above expression like this

Applications: The above expression is generally applied to calculate the weight in grams

of solute for preparation of solutions of different concentrations in molarity and volumes

of analyte like this.

Example: 1.1. Prepare 0.1M NaOH solution of 250ml volume.

To prepare 0.1M NaOH solution of 250ml volume, the job is to calculate weight of

NaOH. It can be calculated by using the above express as

As we know Molecular Mass of NaOH = 23+16+1 = 40amu

So feed the values in the above expression as

Weight in grams of NaOH = 1g

It means to prepare 0.1M solution of NaOH of 250ml volume capacity we need to

dissolve 1gram weight of NaOH that we calculated with the help of above expression

Normality

It is also a unit of concentration and denoted by N. It can be defined as the number of

equivalents of solute dissolved per unit volume of solution

Equivalent is also a unit of amount and can be defined as

Equivalent mass can be defined as molecular mass of the analyte divided by number of

reacting units as

Number of reacting units in case of acid base reaction called to number of hydrogen or

hydroxyl ions per molecule, while in case of oxidation reduction the no of electron lost or

gained by an atom or molecule.

Substituting the values of number of equivalents of solute in above expression so

Rearranging the above expression as

Weight in grams of solute = Equivalent mass of solute x N x Volume in L

As we know

1L = 1000ml, so replace volume in letter by volume in mL in above expression like this

Applications:

The above expression is used to calculate weight in grams of solute for different

concentrations and volumes of analyte like this.

Example: 1.2. Prepare 0.1N H2SO4 solution of 250ml volume.

Solution:

This example can be solved by using expression as we know

As H2SO4 molecule containing 2 H+ so it equivalent mass will be as

Molecular mass of H2SO4 = 98amu, so put this value in above expression

Equivalent mass=49

So put the values in above expression as

Weight in grams of H2SO4= 1.22g

As H2SO4 is a liquid in case of liquids instead of mass we are taking volume, so to

calculate the volume we should use expression of density as

Rearranging the above expression as below

Substituting the values

Volume in mL = 2.24mL

But we know the percent purity of available H2SO4 is 98%. It means if we need 98mL of

pure H2SO4 that will be present in 100mL of available bottle H2SO4. Now 2.24mL of pure

H2SO4 will be present in how much volume of bottle H2SO4?

We can calculate it with the help of dimensional analysis i.e.

It means to prepare 0.1N H2SO4 solution of 250ml volume capacity we need to dissolve

2.29ml of available bottle H2SO4.

Formality

It is a unit of concentration and denoted by “F”. It can be defined as the number of formals

of solute dissolved per unit volume of solution

Formal is unit of amount and can be defined as

Substituting the values of number formals of solute in above expression as

Rearranging the above expression as

As we know

1L = 1000ml, so replace volume in letter by volume in mL in above expression like this

Applications: The above expression is generally applied to calculate the weight in grams

of solute for preparation of solutions of different concentrations in formality and volume

of analyte like this.

Example: 1.3. Prepare 0.1F NaCl solution of 250ml volume.

Solution:

This example can be solved by using expression as we know

So put the values in the above expression as

Weight in grams of NaCl = 1.46g

It means to prepare 0.1F solution of NaCl of 250ml volume capacity we need to dissolve

1.46gram weight of NaCl.

Molality

It is also a unit of concentration and denoted by “m”. It can be defined as number of moles of solute dissolved per Kg of solvent.

Mole is unit of amount and can be defined as

Substituting the values of no of moles of solute in above equation so

Rearranging the above expression as

As we

As we know

1kg = 1000g, so replace mass in kg by mass in g in above expression like this

Applications: The above expression is generally applied to calculate the weight in grams

of solute for preparation of solutions of different concentrations in molality and volumes

of analyte like this.

Example: 1.4. Prepare 0.1m NaOH solution in 250g of solvent.

Solution:

It can be calculated by using the above expression as

As we know Molecular Mass of NaOH = 23+16+1 = 40amu

So feed the values in the above expression as

Weight in grams of NaOH = 1g

It means to prepare 0.1m solution of NaOH in 250grams of distilled water we need to

dissolve 1gram weight of NaOH in 250grams of distilled water.

Molality is independent of temperature.

Percentage Solution (%)

In order to prepare solutions of higher concentrations we use the units of percentage.

There are three types of percentage Solution i.e. weight/volume, weight/ weight and

volume/volume.

a) Percentage Solution Weight/Volume

Percentage Solution weight/volume meant how much weight of solute is dissolved in

100mL volume of solution.

Example: Calculate the mass in grams for preparation 5% solution of NaOH of 250mL

volume.

Solution:

As we know 5% solution of NaOH meant 5grams of NaOH have dissolved in 100mL

volume of solution. Now to calculate the mass in grams for 250mL volume we can do it

with the help of dimensional analysis i.e. similar units cancel each others

So weight of NaOH = 12.5g

It means to prepare 250mL volume of 5% NaOH solution we need to dissolve 12.5g of

NaOH and then dilute it with distilled water upto 250mL volume.

b) Percentage Solution Weight/ Weight

Percentage Solution weight/ weight meant how much weight of solute is mixed with

100g weight of mixture.

Example: Calculate the mass in grams for preparation 5% mixture in NaCl and sand of

500grams weight.

Solution:

As we know 5% mixture in NaCl and sand meant 5grams of NaCl have mixed with

95grams of sand and the total weight of mixture is 100g. Now to calculate the mass in

grams for 500g mixture we can do it with the help of dimensional analysis i.e.

So weight of NaCl = 25g

It means to prepare 500g mixture of 5% NaCl we need to mix 25g weight of NaCl and

475g weight of sand.

c) Percentage Solution Volume /Volume

Percentage Solution volume /volume meant how much volume of solute is dissolved in

100mL volume of solution.

Example: Calculate the volume in mL for preparation 5% solution of HCl of 250mL

volume.

Solution:

As we know 5% solution of HCl meant 5mL of HCl have dissolved in 100mL volume of

solution. Now to calculate the volume in mL for 250mL volume we can do it with the

help of dimensional analysis i.e.

So volume of HCl = 12.5mL

It means to prepare 250mL volume of 5% HCl solution we need to dissolve 12.5mL of

HCl and then dilute it with distilled water upto 250mL volume.

Parts per million (PPm)

Parts per million (PPm) is also a unit of concentration used for preparation of solutions

containing trace amount of solute. Parts per million meant how many parts of solute are

present in one million parts of solution.

For example NaOH solution having concentration 1000ppm. It means that there are 1000

molecules of NaOH are present or dissolved in one million molecules of solution.

It can be prepared as below

1ppm= 1µg/ml or 1ug/g

1000ppm= 1000µg/ml

Applications: For example some body asked to prepare 1000ppm KMnO4 solution of 100ml volume.

To prepare this solution we need to calculate weight in grams of KMnO4

As we know

1ppm= 1µg/ml

So substitute the values in above expression as

As we know

µ= 10-6

So put it in the above expression

Dissolve 0.1g of KMnO4 and dilute it upto 100mL volume with distilled water, so its

concentration will be 1000ppm.

Parts per billion (PPb)

Parts per billion (PPb) is also a unit of concentration used for preparation of solutions

containing trace amount of solute. Parts per billion meant how many parts of solute are

present in one billion parts of solution.

For example NaOH solution having concentration 1000ppb, it means that there are 1000

molecules of NaOH are present or dissolved in one billion molecules of solution.

It can be prepared as below

1ppb= 1ng/ml or 1ng/g

1000ppb= 1000ng/ml

Applications: For example some body asked to prepare 1000ppb KMnO4 solution of 100ml volume.

To prepare this solution we need to calculate weight in grams of KMnO4

As we know

1ppb= 1ng/ml

So substitute the values in above expression as

As we know

n= 10-9

So put it in the above expression

Dissolve 1 x 10-4g of KMnO4 and dilute it upto 100mL volume with distilled water, so its

concentration will be 1000ppb.

Dilution Formula

In some cases concentrated solutions are prepared and then with the help of dilution

formula from those concentrated solutions dilute solutions of our required concentrations

are prepared i.e.

Example: How much volume of 1000ppm KMnO4 solution is required to prepare 100ppm dilute KMnO4 solution of 100mL volume?

Solution:

As we know the dilution formula is

Now substituting the values in the above expression as below

V1 = 10mL

It means take 10mL volume from 1000ppm stock or concentrated solution and then transfer it

into 100mL volumetric flask and dilute it with distilled water its final concentration will be

100ppm.

Stoichiometry

The shortest representation of a chemical reaction in terms of formula of compounds is called

chemical equation, while the shortest representation of a balanced chemical equation in terms of

units of amount is called as stiochiometry.e.g.

Chemical Equation…..Na2CO3 + 2 AgNO3 Ag2CO3 + 2 NaNO3

Stiochiometry……… 1mole + 2mole 1mole + 2mole

Example:

(a) What mass of AgNO3 (169.9 g/mol) is needed to convert 2.33g of Na2CO3 (106.0 g/mol)

to Ag2CO3 (275.7 g/mol)?

(b) What mass of Ag2CO3 will be formed?

Chemical Equation…..Na2CO3 + 2 AgNO3 Ag2CO3 + 2 NaNO3

Stiochiometry……… 1mole + 2mole 1mole + 2mole

Solution:

(a). First of all convert the given mass into moles using expression as

So for 2.33g of Na2CO3 number of moles=?

Molecular mass of Na2CO3=106g/mole

Number of moles of Na2CO3 = 0.02198 moles

As we know from stiochiometric relationship, 1 mole of Na2CO3 react with 2moles of AgNO3

So 0.012198 moles will react with how many moles of AgNO3

So number of moles of AgNO3 = 0.0439 moles

Mass is grams of AgNO3 = number of moles x molecular mass of AgNO3

Mass in grams of AgNO3 = 0.0439 x 169.9 = 7.47grams of AgNO3

b). Mass of Ag2CO3 formed?

As from stiochiometric relationship we know 1mole of Na2CO3 form one mole of Ag2CO3

So 0.01219 moles will also produce 0.01219 mole of Ag2CO3

Now Mass is grams of Ag2CO3 = number of moles x molecular mass of Ag2CO3

= 0.01219 x 275.7 = 6.06g of Ag2CO3

Q 12: What mass of Ag2CO3 (275.7 g/mol) is formed when 25.0mL of 0.200M to AgNO3 are

mixed with 50.0mL of 0.0800M Na2CO3

Balance chemical equation is given as bellow

Chemical Equation…..Na2CO3 + 2 AgNO3 Ag2CO3 + 2 NaNO3

Solution:

Number of millimoles of AgNO3 = M x VmL = 25 x 0.200 = 5 millimoles

Number of millimoles of Na2CO3 = M x VmL = 50 x 0.0800 = 4 millimoles

As there are two reactants

Firstly we have t calculate the amount of Ag2CO3 using the amount of reactant AgNO3

As from Stoichiometry

Mass in milligrams of Ag2CO3 = moles x M. Mass of Ag2CO3 = 2.5 x 275.7 =689.25mg

As

1g = 1000mg

So

689.25mg = 6.8925g of Ag2CO3

Now for second reactant Na2CO3 the number of millimoles of Ag2CO3

As from stoichiometric relationship given above

Mass in milligrams of Ag2CO3 = moles x M. Mass of Ag2CO3 = 4 x 275.7 =1102.8mg

As

1g = 1000mg

So

1102.8mg = 11.02g of Ag2CO3

As AgNO3 is the limiting reactant produce least amount of product so the amount of Ag2CO3 produced is 6.25g

Standard Solution

The solution that is having exact and known concentration is called standard solution. Standard solutions can be prepared with the help of primary standards.

Primary Standards

Primary standards are those chemical reagents having high percent purity, stability toward air,

having high molecular mass, readily solubility in the solvent, having medium cost and readily

availability. A few primary standards are as follow,

Potassium hydrogen phthalate (KHP) is used as a primary standard for standardization of

NaOH

Na2CO3 is used as a primary standard for standardization of HCl

Na2C2O4 is used as a primary standard for standardization of KMnO4

Zn pellets or Mg ribbons are used as a primary standard for standardization of EDTA

Standardization

Standardization is a process used for preparation of solutions of known concentrations. In this

process the solutions of primary standard as well as analyte are prepared. Then known volume

from standard solution with the help of pipette is taken in the titration flask. In order to locate the

end point of this titration one drop of indicator solution is also added to this solution in the

titration flask and it is titrated against analyte solution that is taken in the burette. The end point

will be that point at which indicator shows color change and at that point titration should be

stopped and the volume used from burette should be measured and then using the relationship of

millimoles or milliequivalent the unknown concentration can be calculated as bellow,

Millimoles of analyte = Millimoles of primary standard solution

M1V1 = M2V2

Secondary Standard Solution

Secondary standard solution is that solution used for further standardization of solution having not exact known concentration. The preparation of secondary standard solution is done with the help of primary standard solution. After standardization with primary standard then we call it secondary standard solution and can be used for further standardization. For example the NaOH solution after standardization against KHP is now a secondary standard solution and this solution can be used for standardization of HCl solution.

Calculation of pH

Acids are those chemical reagents on dissolution in water produce hydrogen ion (H+). Acids may

be strong acids like HCL, H2SO4, and HNO3 or may be weak acids like acetic acid etc. The

strong acid is that which completely dissociate into hydrogen ion while the weak acid is that

which partially dissociate into hydrogen ion. For acidic solution its strength of acidity can be

calculated in term of pH. Experimentally pH can be measured by using an instrument called pH-

meter.

In mathematics p is meant negative log

So pH can be defined as negative log of hydrogen ion concentration i.e.

For strong acidic solution the pH can be calculated as

Example: Calculate the pH for 0.1M HCl solution

Solution:

As we know HCl is strong acid and it completely dissociate into hydrogen ion and produce 0.1M of H+

In this example the hydrogen ion concentration is 0.1M so putting the value in above expression As we know for strong acid pH

So putting values

Example: Calculate the pH of 0.1N H2SO4 solution.

Solution:

As we know in case of strong acid,

As H2SO4 is strong acid completely dissociate and producing 0.1N hydrogen ion concentration

so putting the magnitude of hydrogen ion concentration in the above pH expression as

pH calculations for weak acids

Weak acids are those acids that dissociate partially into hydrogen ion when dissolve in water. For example acetic acid

In case of weak acid we cannot write pH as

For example acetic acid it does dissociate as below

The above reaction shows that acetic acid dissociates partially and equilibrium is established

between acetic acid and hydrogen ions and acetate ion. This equilibrium condition can be

expressed by equilibrium constant as

Re arranging the above expression as

As at equilibrium state the hydrogen ion concentration is equal to acetate ion concentration i.e.

So putting this acetate ion concentration in the above expression as below

Or rearranging the above expression as

As we know

Or

Example: Calculate the pH for 0.001N CH3COOH solution of 250ml volume. Ka value for

acetic acid is 1.75 x 105- at 25 Co

Solution:

As we know CH3COOH is a weak acid and in case of weak acid pH can be calculated by using

the expression as given below

So substituting the values in this expression

Q: Calculate the pH for a mixture of solutions in that 50ml volume of 0.1M HCl was mixed with

25mL volume of 0.1M NaOH solution and 25mL volume of water (5points).

Solution:

Millimole of HCl = M x VmL = 0.1 x 50 = 5 millimole

Millimole of NaOH = M x VmL = 0.1 x 25 = 2.5 millimole

Millimole of HCl left untreated = 5 - 2.5 = 2.5millimole

Concentration of H+ = 2.5/100mL = 0.025M

pH = -log [H+] =-log [0.025] = 1.65

Calculation of pOH

So pOH can be defined as negative log hydroxyl ion concentration i.e.

For basic solution its strength of basicity can be measured in term of pOH. Bases are those

chemicals that can produce hydroxyl ion (-OH) in water. As we know bases may be strong bases

like NaOH, KOH, etc or may be weak bases like Ammonium hydroxide etc. The strong base is

that which completely dissociate into hydroxyl ion while the weak base is that which partially

dissociate into hydroxyl ion. For strong basic solution the pOH can be calculated as

Example: Calculate the pOH and pH for 0.01N NaOH of 250ml volume.

Solution:

As we know

So

As we know for water dissociate as below

But the amount of [ H2O] is too much remain nearly constant so we can write it as

So

Now taking negative log on both sides of the above expression

As we know

So the above expression can be written as

As we know Kw value for water is 1 x 10-14 at 25 Co

So

So for this calculation

Calculate the pH of 0.01N NH4OH solution its Kb is 1.75 x 10-5 at 25C0.

Ans:

As we know

pOH = -log [ OH-]

But

In case of Weak base

Substituting the values in above expression

[ OH-] = 4.18 x 10-4 M

pOH = -log [ OH-]

So

pOH = -log [4.18 x 10-4]

pOH = 3.31

But for pH calculation

Rearranging the above expression

Q2: Calculate the pH for a solution in that 50ml volume of 0.01M CH3COOH solution

was mixed with 50ml volume of 0.01M NaOH solution where Ka is 1.75 x 10-5 and Kw is 1

x 10 -14 at 25C0 (5points).

Solution:

m.mole of NaOH = M × Vml = 0,1 × 50 = 5 m.mole

m.mole of acid = M × Vml = 0,1 × 50 = 5 m.mole

CH3COOH + NaOH = CH3COONa

CH3COONa CH3COO - + Na+

CH3COO- + H2O CH3COOH + OH-

[CH3COO-] = m.mole of salt ∕ VT = 5 ∕ 100 = 0.05 M

POH = -Log [OH-]

POH= -Log(5.3×10-6) = 5.27

PH = Pkw – POH = 14 – 5.27 = 8.72

PH = 8.72

Buffer solutions

Buffer solutions are those solutions when they are added to some other solution they resist to

change in pH if small amount of strong acid or strong base is added to that solution. Or

We can say the buffer solution has the property to control the pH of that solutions to which it has

been added.

Chemical Composition of a buffer solution

Buffer solution are chemically made of either weak acid or weak base and the salt derived from

that weak acid, or weak base e.g. buffer solution of CH3COOH/CH3COONa and the other one

NH3OH/NH4Cl

Buffer action

The mechanism how the buffer solution control the pH is that as we know buffer solution

containing two components one is weak acid or weak base and the other is its salt.

For example if an acidic buffer solution has been added a few ml of strong acid, so it will react

with the salt component of the buffer solution and will change it back to weak acid so its effect

on the pH change will be less and negligible i.e.

If few ml of strong base like NaOH has been added to this buffer solution so that will react with

the acidic component of the buffer solution and will produce salt that is again neutral solution i.e.

So we can see that the effect of strong acid or strong base that has been added to buffer solution

has been neutralized either by reacting with salt component or with acidic or basic component of

that buffer solution.

Criteria for Selection a buffer solution of a required pH

In order to prepare buffer solution for a required pH range, it is required that we should select

either a buffer mixture of weak acid or weak base and their pKa or pKb values should be having

values very close to the required pH range in that we want to have control the pH of a solution.

For example we need to control pH of a solution near to 5 pH. As we know this pH range is on

acidic side so first we should select weak acid and its salt for preparation of this buffer mixture.

As acetic acid is having pKa value i.e. pKa = 4.76, so we will select acetic acid and sodium salt

mixture for preparation of this buffer solution of pH 5.

Calculation the pH of a buffer solution

The pH of a buffer solution can be calculated by using Handerson Hasselbalch equation i.e.

In case of acidic buffer solution the Handerson Hasselbalch equation is written as

And for basic buffer solution the Handerson Hasselbalch equation is written as

Example: Calculate the pH of a solution that is 0.01N in CH3COOH and 0.02N in CH3COONa.

Ka value for acetic acid is 1.75 x 105- at 25 Co

Solution:

This can be solved by using Handerson Hasselbalch equation. As for weak acid the Handerson

Hasselbalch equation is

For acetic acid

Putting the values in the above expression

As

So

Example: Calculate the pH of a solution that is 0.200M in NH3 and 0.300M in NH4Cl. The

dissociation constant vale kb for NH3 is kb= 1.75 x 10-5 at 25 Co

Solution:

This can be solved by using Handerson Hasselbalch equation. As NH3 is weak base and for basic

buffer solution the Handerson Hasselbalch equation is written as

So for NH3

Putting the values in the above expression

As

So

But for calculation of pH

Rearranging the above expression

Buffer Capacity

Buffer capacity is defined as the number of moles of a strong acid or a strong base that causes

the changes of pH of liter buffer solution by 1 pH unit.

So a buffer solution that is composed of concentrated mixture solution of both the components so

It means its buffering capacity will be also high and will be neutralize high amount of strong acid

or strong base to bring change in pH.

Chapter 2

Volumetric Techniques (Titrations)

Volumetric techniques are also called titrations are a group of classical quantitative

analytical techniques used to determine the unknown amount or concentration of an

analyte solution. Titrations are based on volume measurement therefore named as

volumetric techniques.

Procedure of Titrations

Titrations involve the slow addition of one solution where the concentration is known

called standard solution to a known volume of another solution where the concentration

is unknown called analyte until the reaction reaches a desired level. The point at which all

the amount of analyte is consumed and the amount of standard solution becomes equal to

the amount of analyte solution is called the equivalence point. In order to locate the

equivalent point indicators or instruments are used. The point at which the indicators give

color change is called end point. At end point the volumes of both analyte and standard

solutions are measured by using volume measuring equipments like pipettes and burettes.

Not every titration requires an indicator. In some cases, either the reactants or the

products are strongly colored and can serve as the "indicator". For example, a redox

titration using potassium permanganate (pink/purple) as the titrant does not require an

indicator. When the titrant is reduced, it turns colorless. After the equivalence point, there

is excess titrant present. The equivalence point is identified from the first faint persisting

pink color (due to an excess of permanganate) in the solution being titrated.

Calculations in Titrations

Using the relationship of millimoles or millieqvivalent the unknown amount of analyte is

calculated like this

As units of amount are millimole or millieqvivalent and we know number of millimoles

or number of millieqvivalent are calculated by the relationship as

And the

Putting the values in the above expression as below

Or to calculate weight or mass in grams of analyte the following relationship is used as

bellow

Equipments used in titration

During titration several types of volumetric glass wares are used. They all are designed to

help measure volume of a liquid.

These are volumetric flasks, burettes and pipettes. They are characterized by a high

accuracy and repeatability of measurements. Volumetric flask is used to dilute original

sample to known volume, so that it contains exact volume. Pipettes are used to transfer

know volume of the solutions. Burettes are used to add known volume of titrant to the

titrated solution and they have scale on the sides, so that you can precisely measure

volume of the added solution. Burette is similar to the pipette, as it is designed to measure

volume of the delivered liquid, but it can measure any volume of the solution.

Two other types of volumetric glass are graduated pipettes and graduated cylinders.

These are too designed to deliver requested amount of solution and they have a scale on

the side. However, their accuracy is usually much lower than the accuracy of volumetric

glass described above. They are used to measure amounts of auxiliary reagents, like

buffers.

Usually when measuring the volumes of transparent solution, the bottom of the concave

meniscus must be precisely read on a calibration mark. To make reading of the meniscus

position easier we can use piece of paper with a horizontal black stripe, about an inch and

half wide. If paper is hold half an inch behind a burette with a stripe about a half an inch

below meniscus, solution surface seems to be black and is much easier to see.

In the case of dark solutions (like permanganate), that won't let you see through,

meniscus is invisible, and you should align top of the solution with the calibration mark.

For obvious reasons this procedure works only for burettes.

Types of Titration

There are different types of titration like acid base titration, redox titration,

complexometric titration, precipitation titration, back titration etc

Acid Base Titration

Acid-base titrations are based on acid base reactions and are also called neutralization

titration.

Acid-base titrations are used to determine the unknown amount of most acids and bases.

For example we can use acid-base titration to determine concentration of hydrochloric

acid, sulfuric acid, acetic acid, as well as bases like sodium hydroxide, ammonia and so

on. In some particular cases, when solution contains mixture of acids or bases of different

strengths, it is even possible to determine in one titration composition of a mixture i.e.

sodium hydroxide and sodium hydrogen carbonate mixture.

Most commonly used reagents are hydrochloric acid and sodium hydroxide. Solutions of

hydrochloric acid are stable; solutions of sodium hydroxide can dissolve glass and absorb

carbon dioxide from the air, so they should be not stored for long periods of time. These

solutions can be standardized with the help of primary standard solution. There are many

primary standard substances that can be used in acid base titrations. Those most popular

are sodium carbonate Na2CO3, borax (disodium tetraborate decahydrate) Na2B4O7·10H2O

and potassium hydrogen phthalate KHC8H4O4, often called simply KHP.

Type of indicator depends on several factors. One of them is the equivalence point pH.

Depending on the titrated substance and titrant used this can vary, usually between 4 and

10. However, even if it is often possible (see list of pH indicators) we are rarely selecting

indicator that changes color exactly at the equivalence point, as usually increase of

accuracy doesn't justify additional costs. Thus in practice you will probably use

phenolphthalein when NaOH is used as the titrant and methyl orange when titrating with

the strong acid.

Before proceeding with the end point detection discussion we should learn a little bit

about the pH indicators behavior.

Acid Base Indicators

The chemical natures of indicators those are used in acid base titration for end point

detection are either weak acids or weak bases because in the presence of strong acid or

base they will be present unreacted. When they ionize produce conjugate base or acidic

ions. The color of unionized form of acid base indicators is different from ionized form.

So in this way it indicates about the end point of titration. Indicator dissociation can be

described by the reaction equation as bellow

For example in case of phenolphthalein indicator the unionized form is colorless while the ionized form is pink colored.

Where in the above expression “HPn” is used for unionized form of phenolphthalein and “Pn-” is used for ionized form.

Let's call its acid dissociation constant KInd:

1

This equation can be easily rearranged to important form, showing ratio of concentrations of both forms of the indicator:

2

Observed color of an indicator is a mixture of colors of both forms. At pH=pKInd both forms concentrations are identical (pH-pKInd=0, 100 = 1). When pH is one unit below pKInd, concentration of HInd is 10 times higher than concentration of Ind-, when pH is one unit above pKInd - concentration of HInd is 10 times smaller than concentration of Ind -. If you will consult pH indicator table you will notice that in most cases it lists about 2 pH units distance between pure colors of an indicator. That's because for most hues sensitivity of human eye is too low to differentiate between colors of solution containing less then 10% of one form of the indicator.

As pH indicators are weak acids or bases, they have to react with titrant after finishing the amount of analyte and they also modifiy titration result. Luckily amount of indicators used are so small, that in most cases they can be safely ignored. For example phenolphthalein is used. We usually add about 1-2 drops of this indicator solution to titrated sample.

List of few commonly used acid base indicators is given as below

pH indicators used for end point detection

Indicator namepH

colorpH

colorprepared as

Methyl violet0.1

yellow2.7

violet0.05% water

Cresol red0.2red

1.8yellow

0.1% water

Thymol blue1.2red

2.8yellow

0.05% water

2,4-Dinitro phenol2.8

colourless4.7

yellow0.1% ethanol

Congo red3.0

blue5.2

yellow/orange0.1% water

Methyl orange3.1red

4.4yellow/orange

0.1% water

Bromocresol green3.8

yellow5.4

blue0.1% water

Methyl red4.4red

6.2yellow/orange

0.1% ethanol

Chlorophenol red4.8

yellow6.4

purple0.1g in 24 mL of 0.01 M NaOH, dilute to

250 mL

Litmus5.0red

8.0blue

0.5% water

Bromocresol purple5.2

yellow6.8

purple0.05% water

Bromothymol blue6.0

yellow7.6

blue0.05% water

Phenol red6.4

yellow8.2

red/violet0.05% water

Neutral red6.8red

8.0orange

0.01% in 50% v/v ethanol

Creosol red7.0

orange8.8

purple0.1% water

Thymol blue8.0

yellow9.6

blue0.05% water

Phenolphthalein 8.2 9.8 0.5% ethanol

colourless red/violet

Thymolphthalein9.3

colourless10.5blue

0.2% ethanol

Alizarin yellow GG10.0

bright yellow12.1

brown/yellow0.1% ethanol

How to choose the right indicator in acid-base titration?

Selection of indicators is made on the basis of pH range of the titrating acid and base. The most

ideal indicator is one that shows color change very near to the end point of the titration. To select

a right indicator for indication of end point of titration you match the equivalence point of the

titration with the pKIn of the indicator,

For example, If I titrating CH3COOH against NaOH. Equivalence point will be above pH 7, so,

we have to use phenolphthalein because its pKIn is 9.4 (close to the equivalence point)

Redox Titration

These titrations are based on redox reactions.

Redox reaction is that reaction in that one specie loss electron and the other specie can

gain electron e.g.

KMnO4 + 5Fe2+ + H+ → Mn2+ + 5Fe3+

In the above reaction Mn7+ is reduced to Mn2+ by gaining five electrons from five atoms

of iron and Fe2+ is oxidized to Fe3+.

There are many redox reagents used in redox titrations. To list a few - potassium

permanganate is used for determination of Fe2+, H2O2 and oxalic acid. Potassium

dichromate for determination of Fe2+ and Cu in CuCl. Bromate is used for tin and phenol,

iodides (titrated with sodium thiosulfate) for H2O2 and Cu2+. Cerium (IV) can be used to

determine ferrocyanides and nitrites. There are also many other methods.

Redox indicators

In order to locate the end point in case of redox titration there are three types of indicators

used i.e. true redox indicators, self indicators & specific indicators

Commonly used true redox indicators are substances that can exist in two forms i.e.

oxidized and reduced form that differ in color. Potential at which the substance changes

color must be such that the change occurs close to the equivalence point. Examples of

such substances are ferroin, diphenylamine or nile blue

In the case of one color indicators, potential at which indicator color starts to be visible

depends on the indicator concentration. The most obvious one is while the general idea

that observed color depends on the ratio of concentrations of both reduced and oxidized

forms still holds, ratio of concentrations is not pH dependent, but redox potential

dependent. We can easily calculate ratio of the concentrations of both forms using Nernst

equation:

1

Let's assume as we did in the case of pH indicators that for the complete color change we

have to move from 10:1 to 1:10 concentration ratio. That means we have to move from

the potential

2

to

3

or by

4

at 25 °C (more precisely it should be 118.2 mV, but as we started with an approximate

rule 10:1 to 1:10, such accuracy is not necessary). This is a useful rule of thumb 120 mV

will be enough always. For many indicators reaction requires 2 electrons, so 60 mV

change is enough for the observable color change.

Table below contains some of the popular redox indicators. Note, that reduced forms of

many indicators are colorless that means, that indicator concentration plays important

role.

Redox indicators used for end point detection

indicator name reduced form color

oxidized form color

normal potential at pH 0 (V)

normal potential at pH 7 (V)

Safranin T colorless red 0.24 -0.29

Neutral red colorless red 0.24 -0.33

Indigomonosulfonic acid colorless blue 0.26 -0.16

Phenosafranin colorless red 0.28 -0.25

Indigotetrasulfonic acid colorless blue 0.36 -0.05

Methylene blue colorless green-blue 0.36 ???

Nile blue colorless blue 0.41 ???

Benzidine colorless blue 0.92 ???

Variamine blue B colorless blue 0.69 ???

Diphenylbenzidine colorless violet 0.76 TS

Diphenylamine sulfonic acid

colorless red-violet 0.85 TS

Erioglaucine A green red 1.00 ???

p-Ethoxychrysoidine red light yellow 1.00 TS

Setoglaucine yellow-green light red 1.06 ???

p-Nitrodiphenylamine colorless violet 1.06 ???

Ferroin red light blue 1.06 ???

5-Nitroferroin red-violet light blue 1.25 ???

2,2'-Bipyridine colorless yellow 1.33 TS

Self Indicators: However, in most popular redox titrations there is no need for a special

indicator i.e. potassium permanganate has strong color by itself, small excess of

permanganate is immediately visible, as the permanganate itself has a very strong color.

As we need some excess of the titrant, it makes sense to start with a blank test, to check

what volume of excess titrant has to be added before the color change can be spotted.

Specific Indicators: In the case of iodometric titration, we use starch as indicator and it

is specifically used for this titration. Free iodine adsorbs at the starch surface, changing

its color to blue. Depending on the titration type (and titrant) starch will either allow

determination of the first traces of excess iodine, or determination of the moment when

last traces of iodine disappear. In the latter case it is important to add starch close to the

endpoint, as product of the iodine-starch reaction created when iodine concentration is

high is relatively stable. Iodine itself is colored and its solutions are yellow, but intensity

of the color is usually too low to be useful for endpoint detection.

In the case of bromine titration we can use methyl orange as an indicator - once the

excess free bromine appears in the solution, it will oxidize the indicator and solution

turns colorless. This is an example of application of irreversible redox indicator.

If you want to select an indicator for your method, you can try approach similar to that

described in the acid-base titration end point detection section - calculate redox potential

of your system for 99.9% and 100.1% titration and choose an indicator that changes color

between these values.

Complexometric titration

These titrations are based on complexation reactions.

Most often used reagent is EDTA (EthyleneDiamineTetraAcetic acid). There are also

other similar chelating agents (EGTA, CDTA and so on) used.

In the case of determination of metals detection of the endpoint is mainly based on

substances that change color when creating complexes with determined metals. One of

these indicators is Eriochrome black T, substance that in pH between 7 and 11 is blue

when free, and black when forms a complex with metal, other examples are

pyrocatechin violet and murexide. It is important that formation constant for these

complexes is low enough, so that titrant reacts with complexed ions first.

Probably most popular and universal indicator used in complexometric titrations is

Eriochrome Black T. Complexed form is always wine red and un-complexed form is

blue. Eriochrome Black T solutions are unstable, so it is prepared as a solid, mixed with

NaCl (100 mg of indicator ground with 20 g of NaCl), or as a fresh solution (shelf life

one day).

Similar in its properties, but much more stable (solutions can be kept for up to a year) is

calmagite. It can be used instead of Eriochrome Black T in most titrations.

Other popular indicators are pyrocatechin violet, murexide and PAN. Also sulfosalicylic

acid is used, although it differs from other indicators listed, as it is used only for one

cation (Fe3+) and is a one color indicator.

Precipitation titration

These titrations are based on precipitation reactions.

Ag+ + Cl- → AgCl (s)

Ther are three types of precipitation titrations i.e. Mohr Method, Fajans method &

Volhard method

To detect the end point of titration in Mohr Method, sodium chromate is used as

indicator that reacts with the excess of AgNO3 creating strongly colored red silver

chromate.

Titration reaction

Ag+ + Cl- → AgCl (s)

Indicator reaction

2 Ag+ + CrO42- → Ag2CrO4 (s) red precipitate

In case of Fajans method an adsorption indicator i.e. flourescein is used. In aqueous

solution flourescein partially dissociate into hydronium ion and flouresceinate ion which

is yellow green in color.

But after reaching the equivalence point the flouresceinate ion react with silver ion and

form an intensively red silver salt, which is the indication of end point.

In case of Volhard method (Back titration) Iron (III) serves as an indicator. An excess

amount silver nitrate is added to the chloride solution. The chloride ions react with silver

ion and precipitate as silver chloride. The excess amount of silver ion is determined by

titrating it against standard solution of thiocyanate. After the equivalence point the

thiocyanate ion react with Fe3+ and form a red color complex of FeSCN2+ which is the

indication of end point of this titration.

Titration reaction

Ag+excess + Cl- → AgCl (s) white precipitate

SCN- + Ag+excess →AgSCN(s) white precipitate

Indicator reaction

Fe3+ + SCN- → FeSCN2+ red color

Back titration

Sometimes it is not possible to use standard titration methods. For example the reaction

between determined substance and titrant can be too slow, or there can be a problem with

end point determination.

In such situations we can often use a technique called back titration. In back titration we

use two reagents - one, that reacts with the original sample (lets call it A), and second

(lets call it B), that reacts with the first reagent. How do we proceed? We add precisely

measured amount of reagent A to sample and once the reaction ends we titrate excess

reagent A left with reagent B. Knowing initial amount of reagent A and amount that was

left after the reaction (from titration) we can easily calculate how much reagent A was

used for the first reaction.

Spectroscopy

Spectroscopy is a kind of analytical techniques used for identification as well

quantification (determination the unknown amount) of analyte. It is based on

interaction of electromagnetic radiations with matter. Some time the matter absorbs or

sometimes emits radiations. So in spectroscopy we measure the magnitude of absorbed

or emitted radiations and then relate that magnitude of radiations with the

concentration of analyte species.

Spectroscopy is broadly categories into two classes i.e. Absorption Spectroscopy and

Emission Spectroscopy. In case of absorption spectroscopy we pass electromagnetic

radiations from analyte species and then measure the magnitude of radiation absorbed

by analyte species and then relating the amount of absorbed radiation with the

concentration of analyte species using Beer’s Lambert Law i.e.

A = bC

Where & b are constant so, A C (absorption is directly proportion to concentration

of analyte specie)

While in case of emission spectroscopy we measure the intensity of emitted radiations

and then relating the magnitude of intensity of emitted radiation to the concentration of

analyte species i.e. I C (Intensity is directly proportion to concentration of analyte

specie)

As we know EMR or spectrum consists of different wavelengths or energy regions. For

example x-rays radiations are occurring in the wavelength region of 0.1nm to 10nm,

while the ultraviolet radiations are occurring in the wavelength region from 180nm to

380nm, while the visible radiations are occurring in the wavelength region from 380nm

to 780nm, while the infrared radiations are occurring in the wavelength region from

780nm to 4000nm, while the radio frequency radiations are occurring in the wavelength

region from 10cm to 1m.

The type of spectroscopy in that radiations in x-rays region interact with matter is called

x-rays spectroscopy for example XRD and XRF used for elemental analysis.

The type of spectroscopy in that radiations in ultraviolet and visible region interact with

matter is called UV-Visible spectroscopy is used for quantitive analysis.

The type of spectroscopy in that the radiations interact in infra red region with matter is

called infra red or IR spectroscopy is used for functional group identification purposes.

The type of spectroscopy in that radiations interact in radiofrequency region with

matter is called nuclear magnetic resonance or NMR spectroscopy is used for structure

elucidation of organic compound.

In this course we will be discussing the type of spectroscopy in that the radiations

interact in UV-visible regions only i.e. absorption spectroscopy.

UV-Visible Molecular absorption spectroscopy

The type of spectroscopy in that ultraviolet and visible region radiations interact with

molecular species and absorbed is called UV-Visible molecular absorption spectroscopy.

The energy of radiations in this region is used for excitation of electron in different

molecular levels. The changes depend on the probability of electronic transitions

between the individual energy states of the molecule.

The probability of electronic transitions in a molecule depends on the presence of

multiple bonds in the molecule and on the kind, number and positions of the

substituent groups.

Spectral transitions of electrons associated with absorption of radiation correspond to transitions from binding orbitals to anti-bonding orbitals of higher energy state. The energy of the respective transitions decreases in the following order: 7t

σ → σ*

n → σ*

π → π*

n → π*

Aromatic π → aromatic π*

The sigma to sigma star transitions (o--~ o*) may take place in the far ultraviolet region

of radiation, which is generally not recorded in spectrophotometers. Other transitions

occur in the near ultraviolet and visible regions. The n to Π* transitions are

characterized by high intensity which varies depending on the number and kind of

multiple bonds in the molecule. An increase in the number of conjugated bonds results

in a reduction of the distance between the Π to Π* levels, an increase in the probability

of transition, and increase of intensity of the spectrum recorded.

The color of a molecule is an effect of the presence of chromophoric groups. A

chromophore may be a group of atoms containing easily excitable pi electrons,

including the most important groups for the visible region: the azo group -N=N- and the

p-quinonoid system. Nitro group etc

The features of the absorption spectra change if the so-called auxoehromes (e.g., -NH2,

-NR2, -SH, -OH, -OR) are introduced into the molecules. The presence of free electron

pairs in the auxochromic group that interact with lone pair electrons of the

chromophoric group (e.g., the free electron pair at nitrogen in the-NH2 group) leads to a

state of conjugation which may result in formation of a new absorption band in the

spectrum

An action of a substituent or a solvent may give rise to a shift of absorption band

towards longer wavelengths is called the bathochromic effect, or towards shorter

wavelengths is called the hypsochromic effect. An increase or a decrease of band

intensity is referred to as the hyperchromic or the hypsochromic effect, respectively.

Absorption laws

Spectrophotometric measurements are generally made on solutions, either in water or

in organic solvents, contained in a measuring cell which is placed in the path of a beam

of monochromatic radiation of chosen wavelength.

From the total radiation of intensity Io that impinges upon a layer of solution, one

fraction of the beam Ia is absorbed on passing through the solution, another fraction It

is transmitted, and still another fraction Ir is reflected by the cell walls and scattered:

lo= Ia + l, + lr

The amount of radiation absorbed depends on the thickness of the absorbing layer and

on the concentration of the solution. In the formula derived by the Lambert & Beer for

the absorption of radiations by solution they took into account both the thickness of the

medium layer and concentration. When a parallel beam of monochromatic radiation of

intensity impinges upon a layer of solution a part of the radiant energy is absorbed. The

fraction of radiation absorbed increases exponentially with linear increase of the layer

thickness:

Similarly the absorption of radiation also increase with increase in concentration of

analyte species, so they expressed a relationship in that they showed the relationship

among the absorption, thickness of the layer of the medium as well as concentration of

analyte solution. This relationship is called Beer Lambert Law, It is given as below

Where E is a constant called the molar absorptivity (or absorption coefficient), c is the

concentration of absorbing species (M, in moles per litre), and l is the layer thickness (in

cm).

The equation is a mathematical expression of a fundamental law of spectrophotometry,

the Bouguer-Lambert-Beer law, which states that absorption of radiation depends on

the total number of absorbing centres, i.e., on the product of concentration and layer

thickness of the solution.

In spectrophotometric measurements the thickness of the sample layer is usually

identical to that of the reference solution, and only Beer's law, which relates the

absorbance with the concentration of the sample solution, is of practical significance.

From a practical point of view it is desirable that the solution should follow Beer's law

for the concentration range corresponding to absorbances not exceeding 1 (unity).

Deviations from Beer's law

Deviations from Beer's law may also result from either chemical reasons connected with

the sample, or physical ones connected with the instruments involved.

Spectrophotometric apparatus

The instrument that has been used for measurement of radiation has been absorbed by molecular

specie is called UV-Visible Spectrophotometer. It consist of the following components, radiation source,

monochromator, cuvette, and detector with the data treatment system

1. Radiation sources

In most cases spectrophotometers are equipped with two independent radiation sources:

UV and VIS. The UV source is usually a deuterium- or xenon lamp that emits radiation in the range of

180-400 nm or 190-750 nm, respectively. The sources emitting visible light are tungsten- and halogen

lamps. A feature of the halogen lamps is their wider spectral range, higher radiation intensity, and

longer lifetime. In modem spectrophotometers the exchange between the UV and VIS proceeds

automatically. The increasing use of lasers as high intensity sources of monochromatic radiation is

observed.

2. Monochromator

The principal element of the spectrophotometer is the monochromator which serves for dispersion of

the radiation emitted by the source and isolation of a beam of monochromatic radiation of definite

wavelength. The monochromator comprises a system of slits, a collimator, a light-dispersing element,

and lenses or mirrors to focus the dispersed radiation. The dispersing system is the essential part of the

monochromator. The degree of monochromatization is an important feature of the dispersing element.

Beams of monochromatic radiation or radiation of wavelength comprised within a specified narrow

range are isolated by means of filters, prisms, or diffraction gratings. The beams of radiation of a limited

range of wavelength are separated from the continuous spectra by means of properly selected colour

filters.

Modem spectrophotometers are equipped with diffraction gratings, whose dispersion is independent of

the kind of material used and the wavelength of radiation applied. Gratings of

1,800 and 2,400 grooves/mm are used for the UV region, and those with 600 and 1,200 grooves/mm are

applicable for the visible light. The separation of the grooves, denoted as the grating constant, is the

parameter characteristic for the given grating. The high precision of forming the grooves and the

regularity of their separations are characteristic for holographic

diffraction gratings having up to 6,000 grooves/mm. The substitution of diffraction gratings for prisms

enabled researchers to increase the spectral resolution and to extend the measuring range from 1 to 4

in the absorbance scale. To record a diffraction spectrum in a required wavelength range it is necessary

to change the position of the grating to isolate the beam of a given wavelength. The manual method of

changing the position, used in former instruments, has been replaced by mechanical systems.

3. Measuring cuvettes/ sample holders

Measuring cuvettes, in which sample solutions are placed, are made of various materials depending on

the range of radiation used in the measurement. Measurements in the UV are performed with the use

of quartz cuvettes. Synthetic quartz, which is less contaminated with traces of metals, has better optical

properties. Measurements in the VIS range are made using quartz, glass, or plastic cuvettes. The cuvette

should provide maximum transmission of radiation and definite, precisely known thickness of the light-

absorbing layer. Cuvettes of different thicknesses within the range 5 ~tm - 10 cm are produced. Small

cuvettes capable of accepting samples of volumes down to 100 ~tl are also available. Small volume

cuvettes that enable multiple passage of the beam of radiation are of special interest.The cuvette

material should be resistant to the action of chemicals. The cuvettes are placed in measuring chambers

in special holders that provide accurate and reproducible location of the sample in the path of the

radiation beam. Cuvettes of special design are used for measurements over wide ranges of temperature

and pressure or under conditions of permanent flow.

4. Detectors

After traversing the measuring cuvette the radiation impinges on the detector. The role of the detector

is to convert the energy of the incoming electromagnetic radiation into electrical energy. The signal

transformation should be linear, which means that the electrical signal generated should be

proportional to the optical signal received. This condition is successfully fulfilled by photocells,

photomultipliers, photoresistors and photodiodes.

The operation of photocells and photomultipliers is based on the external photoelectric effect. Photons

impinging on the surface of a photosensitive cathode (photocathode) knock out electrons which are

then accelerated in the electrical field between the cathode and the anode and give rise to electric

current in the outer circuit. The spectral sensitivity of a photocell depends on the material of the

photocathode. The photocathode usually consists of three layers: a conductive layer (made, e.g., of

silver), a semiconductive layer (bimetallic or oxide layer) and a thin absorptive surface layer (a metal

from the alkali metal group, usually Cs). A photocathode of the composition, Ag, Cs-Sb alloy, Cs (blue

photocell), is photosensitive in the wavelength range above 650 nm; for longer wavelengths the red

photocell with Ag, Cs-O-Cs, Cs is used. The response time of the photocell (the time constant) is of the

order of 10 -s s.

Photomultipliers are equipped with several supplementary diodes (dynodes) to which the electrons

emitted from the photocathode are directed. The electrons impinging on the dynodes give rise to the

emission of secondary electrons from the successive dynodes and they thus amplify the signal generated

by a factor of up to 108.

In the photoresistors and photodiodes use is made of the internal photoelectric phenomenon and of

specific properties of semiconducting materials. Photons impinging on the photosensitive element

generate an electrical current, which flows through the photoconductor and is amplified by the effect of

a small applied voltage. The increase of the current intensity is proportional to the intensity of photons

that strike the photosensitive element. The microcrystalline layer of lead(H) sulphide deposited on a

dielectric (glass or quartz) plate may serve as an example of a photoresistor applied in the wavelength

range above 700 nm. Photodiodes are made of two or three layers of semiconducting materials

containing suitable admixtures. Silicon photodiodes are used in the UV-VIS range. Modern

spectrophotometers are equipped with multichannel detecting devices that contain a large number of

photodiodes (a photodiode array) and enable simultaneous

detection over the whole range of the spectrum. Details of the design and the advantages of using such

detectors in spectrophotometric measurements have been presented .

5. Data recording and processing

The application of microprocessors and the rapid development of computer techniques has made it

possible to automate the analytical operations from the step of sampling up to full processing of the

data obtained. In modern spectrophotometers, microprocessors are applied to control many operations

that were formerly operated manually. The functions now realized by microprocessors include the

control of the optical system (lamp and analytical wavelength selection), selection of the kind of data

collected (e.g., absorbance, concentration), zero-adjustment, autocalibration and control of

measurement parameters. The microprocessor determines the equation of the regression curve and

provides statistical processing of the results. It can also be programmed to measure the absorbance, the

% transmittance at a selected wavelength, or the concentration based on the relationship (linear or non-

linear) established between the measured absorbance and the concentration.

The advanced spectrophotometers are coupled with computers that facilitate the recording of results

and the processing of the data obtained. Appropriate software enables the presentation of results on

the display, smoothing of the obtained spectrum, calculation of peak heights with respect to the base-

line, and mathematical processing of the results that provides the possibility of, e.g., resolving signals

owing to individual components of the sample analysed. The development of the computer techniques

has facilitated the identification of the structures of chemical compounds by enabling quick and easy

access to catalogues of UV-VIS spectra.

The data recorded and the results obtained can be stored in the computer memory. This gives the

possibility of comparing the obtained results and evaluating their quality by rapid comparison with

greater numbers of data. A critical evaluation of the obtained results always remains the task of the

analyst.

Spectrophotometric technique

If the value of the molar absorptivity, e, for the wavelength used in measurement of absorbance of the

given system is known, it is possible to determine directly the concentration of the analyte by means of

an equation based on Beer's law. The value of e is determined from the measurement of absorbance of

several solutions containing precisely known amounts of the analyte under conditions identical to those

used in the measurement of the sample solution.

In analytical practice, the concentration of the given analyte is, in most cases, determined by the

standard curve technique. The technique is based on the determination of the relationship between the

absorbance and the analyte concentration under the measuring conditions. The relationship is given in

terms of the regression equation, or graphically in the form of a standard curve. For systems that obey

Beer's law this curve is a straight line.

STATISTICAnalyzing Data

The mean, median and mode of a data set are collectively known as measures of central

tendency as these three measures focus on where the data is centered or clustered.  To

analyze data using the mean, median and mode, we need to use the most appropriate

measure of central tendency.  The following points should be remembered:

The mean is useful for predicting future results when there are no extreme values

in the data set. However, the impact of extreme values on the mean may be

important and should be considered. E.g. The impact of a stock market crash on

average investment returns.

The median may be more useful than the mean when there are extreme values in

the data set as it is not affected by the extreme values.

The mode is useful when the most common item, characteristic or value of a data

set is required.

Measures of Central Tendency (Mean, Median and Mode)

There are three measures i.e. mean, median and mode are used to obtain

information about central value or most important value in the data set.

Mean

The mean (or average) of a set of data values is the sum of all of the data values divided

by the number of data values.  That is:

Example 1

The marks of seven students in a mathematics test with a maximum possible mark of 20

are given below:

     15     13     18     16     14     17     12

Find the mean of this set of data values.

Solution:

So, the mean mark is 15.

Symbolically, we can set out the solution as follows:

So, the mean mark is 15.

Median

The median of a set of data values is the middle value of the data set when it has been

arranged in ascending order. That is, from the smallest value to the highest value.

Example 2

The marks of nine students in a geography test that had a maximum possible mark of 50

are given below:

     47     35     37     32     38     39     36     34     35

Find the median of this set of data values.

Solution:

Arrange the data values in order from the lowest value to the highest value:

     32     34     35     35     36     37     38     39     47

The fifth data value, 36, is the middle value in this arrangement.

Note:

In general:

If the number of values in the data set is even, then the median is the average of the two

middle values.

Example 3

Find the median of the following data set:

     12     18     16     21     10     13     17     19

Solution:

Arrange the data values in order from the lowest value to the highest value:

     10     12     13     16     17     18     19     21

The number of values in the data set is 8, which is even.  So, the median is the average of

the two middle values.

Alternative way:

There are 8 values in the data set.

The fourth and fifth scores, 16 and 17, are in the middle.  That is, there is no one middle

value.

Note:

Half of the values in the data set lie below the median and half lie above the

median.

The median is the most commonly quoted figure used to measure property

prices. The use of the median avoids the problem of the mean property price

which is affected by a few expensive properties that are not representative of the

general property market.

Mode

The mode of a set of data values is the value(s) that occurs most often or the value

which repeat itself in data set many times.

The mode has applications in printing.  For example, it is important to print more of the

most popular books; because printing different books in equal numbers would cause a

shortage of some books and an oversupply of others.

Likewise, the mode has applications in manufacturing.  For example, it is important to

manufacture more of the most popular shoes; because manufacturing different shoes in

equal numbers would cause a shortage of some shoes and an oversupply of others.

Example 4

Find the mode of the following data set:

     48     44     48     45     42     49     48

Solution:

The mode is 48 since it occurs most often.

Note:

It is possible for a set of data values to have more than one mode.

If there are two data values that occur most frequently, we say that the set of

data values is bimodal.

If there is no data value or data values that occur most frequently, we say that

the set of data values has no mode.

Measures of Dispersion (Range, Deviation and Standard Deviation)

Dispersion. Dispersion refers to the spread of the values around the central tendency.

There are three measures i.e. range, deviation and standard deviation are used to obtain

information about dispersion, variation or spread of a data set.

When assessing the variability of a data set, there are two key components:

1. How spread out are the data values near the center?

2. How spread out are the tails?

Range

Range is a rough measure of dispersion. It can be obtained by subtracting the largest

value from the smallest value in a data set. Note that this measure is based only on the

lowest and highest extreme values in the sample. The spread near the center of the data

is not captured at all.

Range = Largest value – Smallest value

In our example distribution, the high value is 36 and the low is 15,

So the range is 36 - 15 = 21.

Standard Deviation

The Standard Deviation is a more accurate and detailed estimate of dispersion. Standard

deviation is the square roots of the sum of the squared differences between each score

and the mean average of all scores.

For a population the formula is:

For example we have a data set as,

15, 20, 21, 20, 36, 15, 25, 15

to compute the standard deviation, we first find the deviation for each value i.e.

We know from above that the mean is 20.875. So, the differences from the mean are:

X1=15 - 20.875 = -5.875

X2=20 - 20.875 = -0.875

X3=21 - 20.875 = +0.125

X4=20 - 20.875 = -0.875

X5=36 - 20.875 = 15.125

X6=15 - 20.875 = -5.875

X7=25 - 20.875 = +4.125

X8=15 - 20.875 = -5.875

Notice that values that are below the mean have negative discrepancies and values above

it have positive ones. Next, we square each deviation d2:

d2

-5.875 * -5.875 = 34.515625

-0.875 * -0.875 = 0.765625

+0.125 * +0.125 = 0.015625

-0.875 * -0.875 = 0.765625

15.125 * 15.125 = 228.765625

-5.875 * -5.875 = 34.515625

+4.125 * +4.125 = 17.015625

-5.875 * -5.875 = 34.515625

Now, we take the summation of the above square of deviation. Here, the sum is 350.875.

Next, we divide this sum by the number of scores minus 1. Here, the result is 350.875 / 7

= 50.125. This value is known as the variance. To get the standard deviation, we take the

square root of the variance (remember that we squared the deviations earlier). This would

be SQRT(50.125) = 7.079901129253.

Standard deviation (S) = 7.079901129253

.

WHAT DOES STANDARD DEVIATION MEAN?  The standard deviation statistic is

a number that marks a distance on the measurement scale.  In very general terms it is the

average difference between each value and the mean average.  A standard deviation is

central to many of the statistics used to make inferences and test hypotheses.

HOW IS STANDARD DEVIATION INTERPRETED?  A calculated standard

deviation is an estimate of how values are distributed away from the mean average.  If

this distribution is approximately normal (bell shaped curve), then .34 (34%) of the cases

will occur within one standard deviation.  Also, if one adds one standard deviation to the

mean and subtracts one standard deviation from the mean the between these two numbers

it is estimated that 68% of the cases will occur.  This range give a reasonable range to use

when discussing where about 2/3rds of the cases will be found.  In more advanced

interpretations a researcher may use a fraction of the standard deviation and a normal

distribution table to estimate a different proportion of the cases.

Errors in Chemical Analyses

ERRORS are caused by uncertainties in measurements.   These uncertainties come from

several sources, some can be controlled and minimized while others can not.  The

ultimate result of these uncertainties is that the true value of a measurement can NEVER

be known exactly!

Precision

Refers to the reproducibility of measurements or the closeness of results measured in

exactly the same way. In other words, it is the grouping of data.

Accuracy

Is the closeness of the measurement to its true or accepted value.

Absolute error

The difference between the measured value and the true value

It has a sign (+/-).

Relative error

The absolute error divided by the true value. It has a has a sign (+/-)

Systemic Errors

Systematic errors can come from several sources. They can be classified as instrument

errors, method errors and personal errors.

Instrument errors are due to imperfections in measuring devices and instabilities in

power supplies. They can be detected and minimized by calibrating the instrument.

Method errors are caused by non-ideal chemical or physical behaviors. These may

include:

Slowness of reactions

Instability of certain species

Nonspecificity of most reagents

Possible occurrence of side reactions

Method errors can be detected by using the following techniques:

Analysis of standard reference materials (SRMs)

Independent analysis

Blank determinations (performing all steps of an analysis in the absence of

sample)

Variation in sample size (identifies constant errors)

Personal errors can be due to personal bias and prejudice and physical limitations

and handicaps. Personal errors can be minimized through personal discipline and

training.

Systematic errors can also be classified as either proportional errors or constant errors.

Proportional errors either decrease or increase in proportion to the size of the

sample. The source for these errors is the presence of interfering contaminants in

the sample

Constant errors are independent of the size of the sample being analyzed. They

can be minimized by using as large a sample as possible.

RANDOM ERRORS

Random errors are very small errors caused by uncontrollable variables that cannot be

positively identified. The overall effect is that it causes replicate measurements to

fluctuate randomly around the mean. If we look at calibration data for a 10ml pipet, you

will notice that the measurements are not all exactly the same.

10 ml Pipet Calibration Data

Trial Volume,ml Trial Volume,ml Trial Volume, ml

1 9.988 18 9.975 35 9.976

2 9.973 19 9.980 36 9.990

3 9.986 20 9.994 37 9.988

4 9.980 21 9.992 38 9.971

5 9.975 22 9.984 39 9.986

6 9.982 23 9.981 40 9.978

7 9.986 24 9.987 41 9.986

8 9.982 25 9.983 42 9.982

9 9.981 26 9.982 43 9.977

10 9.990 27 9.991 44 9.977

11 9.980 28 9.981 45 9.986

12 9.989 29 9.978 46 9.978

13 9.978 30 9.969 47 9.983

14 9.971 31 9.985 48 9.980

15 9.982 32 9.977 49 9.983

16 9.983 33 9.976 50 9.979

17 9.986 34 9.983

We can assume that random errors are the only source of errors in this pipet calibration

experiment. There are many possible sources of the random errors. They may include:

Visual judgements

Variations in drainage time

Variations in the angle of the pipet

Temperature fluctuations

o Affects the pipet volume

o Affects the liquid viscosity

o Affects the balance performance

Vibrations and drafts

If small ranges are assigned and the number of values falling within each of the ranges is

counted and plotted, the resulting graph is called a Frequency Distribution Graph or

Histogram.

You will notice that a large number of the measurements fall between 9.978 and 9.981

ml.  As the distance from this "central" range increases, the number of measurements in

each of the successive ranges decreases.    There are approximately the same number of

measurements above the "central" range as there are below it.   The heavy line on the

figure is a general representation of the Gaussian Curve.

The Gaussian Curve can be described by some general properties. One is that the mean

occurs at the central point of highest frequency. Another is that there is symmetrical

distribution of deviations around the mean. If we were to evaluate an infinite number of

measurements which only had random errors, we would find the following:

68.3% of the data is within +/- 1

95.5% of the data is within +/- 2

99.7% of the data is within +/- 3